Related papers: The three-loop polarized pure singlet operator mat…
We present the two-loop corrected operator matrix elements contributing to the scale evolution of the longitudinal spin structure function $g_1(x,Q^2)$ calculated up to finite terms which survive in the limit $\epsilon = N - 4 \to 0$. These…
The matching relations in the unpolarized and polarized variable flavor number scheme at three-loop order are presented in the single-mass case. They describe the process of massive quarks becoming light at large virtualities $Q^2$. In this…
The $O(\alpha_s^2)$ massive operator matrix elements for unpolarized and polarized heavy flavor production at asymptotic values $Q^2 >> m^2$ are calculated in Mellin space without applying the integration-by-parts method. We confirm…
Recent results on the calculation of 3-loop massive operator matrix elements in case of one and two heavy quark masses are reported. They concern the $O(n_f T_F^2 C_{F,A})$ and $O(T_F^2 C_{F,A})$ gluonic corrections, two-mass quarkonic…
We present results on the calculation of the polarized 2- and 3-loop anomalous dimensions in a massive computation of the associated operator matrix element. We also discuss the treatment of $\gamma_5$ and derive results in the M-scheme.10
New results at four-loop order in perturbative QCD for the first two Taylor coefficients of the heavy quark vacuum polarization function are presented. They can be used to perform a precise determination of the charm- and bottom-quark mass.…
We compute the ${\cal O}(\alpha_s^3)$ virtual QCD corrections to the $\gamma^*\to q\bar q g$ matrix element arising from the interference of the two-loop with the tree-level amplitude and from the self-interference of the one-loop…
We report on the calculation of the three-loop polarized and unpolarized flavor non-singlet and the polarized singlet anomalous dimensions using massless off-shell operator matrix elements in a gauge-variant framework. We also reconsider…
We calculate the quarkonic $O(\alpha_s^2)$ massive operator matrix elements $\Delta A_{Qg}(N), \Delta A_{Qq}^{\rm PS}(N)$ and $\Delta A_{qq,Q}^{\rm NS}(N)$ for the twist--2 operators and the associated heavy flavor Wilson coefficients in…
The real and imaginary part of the vacuum polarisation function $\Pi(q^2)$ induced by a massive quark is calculated in perturbative QCD up to order $\alpha_s^2$. The method is described and the results are presented. This extends the…
Starting at 3-loop order, the massive Wilson coefficients for deep-inelastic scattering and the massive operator matrix elements describing the variable flavor number scheme receive contributions of Feynman diagrams carrying quark lines…
We calculate the unpolarized and polarized three--loop anomalous dimensions and splitting functions $P_{\rm NS}^+, P_{\rm NS}^-$ and $P_{\rm NS}^{\rm s}$ in QCD in the $\overline{\sf MS}$ scheme by using the traditional method of…
We present the results of our QCD analysis for polarized quark distribution and structure function $xg_1 (x,Q^2)$. We use very recently experimental data to parameterize our model. New parameterizations are derived for the quark and gluon…
We report on recent progress in calculating the three loop QCD corrections of the heavy flavor contributions in deep--inelastic scattering and the massive operator matrix elements of the variable flavor number scheme. Notably we deal with…
The one-loop NLO radiative corrections to the observables in polarized DIS using assumption that a quark is an essential massive particle are considered. If compared with classical QCD formulae the obtained results are identical for the…
We consider the three-loop singlet diagrams induced by axial-vector, scalar and pseudo-scalar currents. Expansions for small and large external momentum $q$ are presented. They are used in combination with conformal mapping and Pad\'e…
We use QCD sum rules to determine the twist-two non-singlet operator matrix elements and fixed x structure functions paying particular regard to the estimate of the errors. Particularly for the matrix element determination, we find large…
We present the three-loop QCD+QED mixed corrections to the on-shell quark mass and wave-function renormalization constants through orders $\mathcal{O}(\alpha_s^m\alpha^n)$ with $m+n=3$. We further derive the three-loop relation between the…
We calculate all contributions $\propto T_F$ to the polarized three-loop anomalous dimensions in the M-scheme using massive operator matrix elements and compare to results in the literature. This includes the complete anomalous dimensions…
The unpolarized and polarized massive operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$ contain first-order factorizable and non-first-order factorizable contributions in the determining difference or differential equations…